Ik 



CARDS 



4nd other 



CARDS OF AMUSEMENT, . 



With full explanations and illustrations of 
their construction. 



By GEO. R. PERKINS, LL.D.(^ 



UTICA, N. Y. : 

D. P. WHITE, PRINTER, 171 GENESEE STRJ 
1866. 




AGE GAUDS, 



AND OTHER 



CARDS OF AMUSEMENT, 



WITH FULL EXPLANATIONS AND ILLUSTRATIONS 
OF THEIR CONSTRUCTION. 




By GT^^O. K, PERKINS, LL.D, 



UTICA, N. Y.: 
D. P. WHITE, PRINTER, 171 GENESEE STREIT, 
1866. 



PREFACE. 



The folio wiDg pages are the result of a few 
leisure moment^sgipn to the preparation of cards 
for the arausemem; of some of my friends. As 1 
progressed in my investigations my own interest 
became increased and I finally concluded to give 
my results a permanent form, b}^ securing the 
copyright. And I intend soon to take measures 
for securing the patent right for the construction 
and use of all the various cards which I have 
described and referred to, especially those whicli 
I have denominated the Perforated Cards. 



Utica, May 3, 18G6. GEO. R. PERKINS. 



Entered according to Act of Congress in the j-ear 1866, 
BY GEORGE R. PERKINS, LL. D, 
the Clerk's Office of the Northern District of the 




state of New York. 



AGE CARDS. 



All numbers in the natural series may be pro- 
duced by the combination of the terms of the 
geometrical progression, ], 2, 4, 8, 16, 32, 64 &c 
by addition as follows : ' 



C^SE I. 



1 = 

2 = 
3- 
4= 
5 = 
6r 

7 = 

8 = 
9= 

10= 

11 = 

12 = 

13 = 
14= 
15 = 
16= 
11 = 

18 = 

19 = 
20= 

21 = 

22 ±: 
23;=: 



rl 

-2 

:2+l 
:4 

4+1 

:4+2 
:4 + 2+l 
:8 

:8 + l 
:8 + 2 

^8 + 2 + 1 

:8 + 4 

^8+4+1 
:8 + 4+2 
:8+4+2+l 
16 

16 + 1 

16 + 2 

16 + 2+1 

16+4 

16 + 4+1 

16+4+2 

16 + 4+2+1 



24=16 + 8 

25 = 16 + 8 + 1 

26 = 16 + 8 + 2 

27 = 16+8 + 2+1 

28 = 16 + 8 + 4 
29=16 + 8+4+1 

30 = 16 + 8 + 4+2 

31 = 16 + 8 + 4 + 2+1 

32 = 32 

33 = 32+1 

34 = 32 + 2 

35 = 32+2 + 1 
36=32+4 

37 = 32+4 + 1 

38 = 32+4+2 
S9=32 + 4+2+l 
40=32 + 8 

41 = 32 + 8 + 1 

42 = 32+8 + 2 

43 = 32 + 8 + 2+1 

44 = 32 + 8+4 
46=32 + 8 + 4 + 1 



4 



The natural series of numbers may also be 
produced by the combination of the terms of the 
geometrical progression, 1, 3, 9, 27, 81, &c., by 
addition and subtraction, as follows : 

cj^sm II. 



1 — 1 
1 — 1 


9ft — 0*7 1 1 


9 q T 

£i O i 


9Q — 0*7 _J_ ^ 1 


o — O 


O U — ^ 1 -f- o 


A 9 1 1 

4: d-f- I 


Oi — Z< +0+ 1 


r Q Q 1 

— y — 6 — 1 


— Li + y — O — 1 


D — y — 6 


66 — Z/ +y — f) 


^7 o « 1 1 

< — y — o + 1 


Q A o^7 1 n Oil 

o4: — z<+y — o+l 


Q n 1 

o — y — 1 


oo — z/ + y — 1 


9 = 9 


oD — z < +y 


1 A Q 1 1 


6i — z<+y + i 


ii — y+o — 1 


QQ 1 O 1 9 1 

OO — Li + y + o — 1 


I £i — y + D 


oy — z < + y + 


id — y + d-f-i 


4:U — Z<+y + d+ l 




4i = oi — Z7 — y — d — 1 


15 = 27 — y — o 


4rZ = oi — Li — y — 6 


1d = 27 — y — o+I 


AO Q1 OT O Oil 

4o — oi — z/ — y — o+i 


17 = 27 — 9 — 1 


/I o 1 o^7 rk 1 

44= oi — 27 — 9 — 1 


lb — Li — y 


40 — oi — Li — y 


19=27 — 9 + 1 


46=81-27-9 + 1 


20=27-9 + 3-1 


47 = 81-27-9 + 3-1 


21 = 27-9 + 8 


48 = 81-27-9 + 3 


22 = 27 — 9 + 3 + 1 


49 = 81 — 27 — 9 + 3 + 1 


28 = 27-3-1 


50=81-27-3-1 


24=27-3 


51 = 81 — 27 — 3 


26 = 27-3 + 1 


52 = 81-27-3 + 1 


26=27-1 


53 = 81--- 27-1 


27=27 


&c., &c. 



5 



These numbers may also be produced by addi- 
tion and subtraction of the terms of the series, 
1, 3, 0, 19, 57, 171, ^c. 

This series is partly arithmetical and partly 
geometrical; the lirst three terms 1, 3, 5 are in 
arithmetical progression, the succeeding terms 
19, 57, 171, &:c., are in geometrical progression. 
Using these terms we have as follows : 

C^SE III. 



1=:1 


23 = 19 + 3 + 1 


2=:3- 1 


24=19 + 5 


3 = 3 


25 = 19 + 5 + 1 


4 = 3-r 1 


26=19 + 5 + 3 — 1 


5 = 5 


27 = 19 + 5 + 3 


6 = 5 + 1 


28 = 19 + 5 + 3 + 1 


7=5+3—1 


29 = 57 — 19_5_3_1 


8 = 5 + 3 


30=57-19 — 5 — 3 


9=5+3+1 


31 = 57-19-5-3 + 1 


10 = 19-5-8-1 


32 = 57-19 — 5 — 1 


ll=:19-5-3 


33 = 57-19 — 5 


12 = 19-5-3 + 1 


34=57 — 19-5 + 1 


13 = 19-5-1 


35 = 57 — 19 — 3 


14 = 19-5 


36 = 57-19 — 3+1 


15 = 19 — 5 + 1 


37 = 57-19-1 


16=19-3 


38 = 57 — 19 


17 = 19-3 + 1 


39 = 57-19 + 1 


18 = 19-1 


40=57-19 + 3-1 


19 = 19 


41 = 57-19 + 3 


20 = 19 + 1 


42=57-19 + 3+1 


21 = 19 + 3-1 


43 = 57-19 + 5 


22 = 19 + 3 


&e., &c 



6 



These numbers may also be produced by using 
the terms of the following: series, 1, 3, 5, 10, 20, 

40j Ac, which is partly arithmetical and partly 
geometrical, in this case, however, the only term 
to be subtracted is 1, as follows: 

1 = 1 27 = 20+5 + 3- 

2=3—1 28 = 20 + 5 + 3 

3=3 29 = 20 + 5 + 3 + 1 

4=3 + 1 30=20+10 

5=5 31 = 20+10+1 

6=5+1 32 = 20+10+3 — 1 

7 = 5 + 3-1 33 = 20+10 + 3 

8 = 5 + 3 34=20 + 10+3 + 1 

9 = 5 + 3+1 35 = 20+10 + 5 
10=10 36 = 20+10+5 + 1 

11 = 10+1 37 = 20+10 + 5 + 3-1 

12 = 10 + 3-1 38 = 20+10 + 5 + 3 
13=10 + 3 39 = 20+10+5 + 8+1 
14=10+3 + 1 40 = 40 

15=10 + 5 41 = 40+1 

16=10 + 5 + 1 42 = 40 + 3-1 

17 = 10 + 5 + 3-1 43 = 40 + 3 

18=10+5+3 44 = 40 + 3 + 1 

19 = 10 + 5 + 3 + 1 45 = 40+5 

20=20 46 = 40+5+1 

21 = 20 + 1 47=40 + 5 + 3-1 

22=20+3-1 48=40+5 + 3 

23=20+3 49=40 + 5 + 3 + 1 

24=20+3+1 50=40+10 

25 = 20+5 51=40 + 10+1 

26 = 20 + 5 + 1 &c., &c. 



7 



The natural series of numbers may also bo 
produced by the addition and subtraction of 
other chosen terms, but at the preseHt time we 
propose to confine ourselves to the four cases 
here exhibited. 

O^SE I. 

Arranging the riumbers according to the ele- 
ments used in their formation, that is, we group 
all those numbers together which are formed by 

I the aid of 1, all those formed by the aid of 2, all 

j those formed by 4, &c., as follows: 



(A) 


(B) 


(C) 


(D) 


(E) 


1 


2 


4 


8 


16 


3 


3 


5 


9 


17 


6 


6 




10 


18 


7 


7 


7 


11 


19 


9 


10 


12 


12 


20 


11 


11 


13 


13 


21 


18 


14 


14 


14 


22 


15 


15 


15 


16 


23 


17 


18 


20 


24 


24 


19 


19 


21 


25 


25 


21 


22 


22 


26 


26 


23 


23 


23 


27 


27 


25 


26 


28 


28 


28 


27 


27 


29 


29 


29 


29 


30 


30 


30 


30 


31 


31 


31 


31 


31 



These groups designated by the letters A, B, 
J, D, E, (fee, possess the following property: 



8 



Any luiQibor which is found in any one or 
more of these groups, and not in any of the 
other groups, is obtained by adding the leading 
or first numbers in the groups. As examples: 

The number in groups A and D and not in 
either of the other groups, is 1 + 8 = 9. 

The number in groups A, C and E, is 
1 + 4 + 16 = 21; and iu like manner for other 
numbers. 

Hence, knowing that a particular number is 
onl}'- in one or more of tliese groups, we at once 
know the number. 

The above groups when arranged on separate 
pieces of paper or cards, have been known and 
published as Age Cards. They usually consist 
of seven cards, whose leading numbers are 1, 2, , 
4, 8, 16, 32 and 64, and embrace all the series of | 
natural numbers up to 127. 

A person being asked to select such of tho 
cards as contain the number of 3'ears denoting 
his age, you at once determine this number by 
adding tlie top numbers of the selected cards. 

C^SE II. 

Arranging our groups, or cards, according to 
the elements, 1, 3, 9, 27, 81, &c., observing to , 
make a distinct and separate grouping for the i 
negative values of these terms, which we have 
indicated by the small letters a, h, c, d, &c., as 
follows : 



9 



[_1][_3J [-9] 





(B) 


(C) 


(D) 


" (a) 






[ 1] 


2 


5 


14 


2 


5 


14 


4 


[ -^1 


6 


15 


5 


6 


15 


7 


4 


7 


16 


8 


7 


16 


10 


11 


8 


17 


11 


14 


17 


13 


12 


[ 9] 


18 


14 


15 


18 


16 


18 


10 


19 


17 


16 


19 


19 


20 


11 


20 


20 


23 


20 


22 


21 


12 


21 


23 


24 


21 


25 


22 


18 


22 


26 


25 


22 


28 


29 


32 


23 


29 


32 




31 


30 


38 


24 


82 


38 




34 


31 


34 


26 


35 


84 




37 


38 


35 


26 


38 






40 


39 


36 


[27] 










40 


37 


28 












38 


29 












39 


30 












40 


31 














32 














38 














34 














35 














36 
37 














S8 














39 














40 









1* 



10 



To determine in this case the number on the 
selected cards, we must add the numbers on the 
cards denoted by the capital letters, which are 
included in the brackets — [ ] — and from the sum 
subtract the numbers on the cards denoted by the 
small letters which are in the brackets imme- 
diately over the letters. Exaiiiples: Suppose 
the selected cards tohQ A, B and D, the number 
will be 1 + 3 + 27 = 31. If the cards are D, a 
and c, the number will be 27 — 1 — 9= 17. If 
the cards are C, D and a, the number will be 
3 + 9 + 27 — 1 = 38; and in a similar way for 
other eases. 

By the introduction of two additional cards 
denoted by (E) and (d) whoso values are +81 
and —27, we shall embrace all numbers up to 
121. . 

These nine cards, with a card of explanation,! 
are given on the last pages of this book, two 
cards being printed on each page, so that- they 
may be readily cut out and used as a Puzzle^ 
independent of the other matter. 

In a similar way cards may be formed for the 
other cases here given. 

cj^se: III. 

Arranging our numbers according to the ele- 
ments 1, 3, 5, 19, 67, &c., distinguishing the neg- 
ative values from the positive as in the preceding 
case, we have 



11 











[-1] 


[-S] [- 


-5] 


(A) 


(B) 


(C) 




(a) 


(b) 


(c) 


[ 1] 


2 


[ 5] 


10 


2 


10 


10 


4 


[ 3] 


6 


11 


7 


11 


11 


6 


4 


7 


12 


10 


12 


12 


9 


7 


8 


13 


13 


16 


IS 


12 


8 


9 


14 


18 


17 


14 


15 


9 


24 


15 


21 




15 


17 


21 


26 


16 


26 






20 


22 


26 


17 








23 


23 


27 


18 








25 


26 


28 


[19] 








28 


27 
28 




20 
21 
22 
23 
24 
25 
26 
27 
28 









In this case, if the selected cards are A, 
D and c, the number is 1 + 19 — 5=15; if 
the cards are D, a, b and c, the number is 
19 — 1 — 3 — 5=10; and so for other combination 
of cards. 

By the introduction of two cards (E) and (d,) 
whose vahies are +57 and —19, we shall em- 
brace all numbers up to 85. 



12 



Pfoceediog as in the precediug cases we find: 













[-1] 


(A) 






{^) 




[a] 


[ 1] 


2 




r 1 A 1 


[20] 




4 


[ s] 


6 


11 


21 


7 


6 


4 


7 


12 


22 


1 2 


9 


7 


8 


13 


2S 


17 


11 


s 


9 


14 


24 


22 


14 


9 


15 


15 


25 


2i 


16 


12 


16 


16 


26 


32 


19 


13 


17 


17 


27 


37 


21 


14 


] 8 


IS 


28 




24 


17 


19 


19 


29 




26 


1 8 


25 


SO 


30 




29 


19 


26 


31 


31 




81 


22 


27 


S2 


32 




34 


23 


28 


33 


33 




36 


24 


29 


34 


34 




89 


27 


35 


35 


35 






28 


36 


36 


36 






29 


37 


37 


87 






32 


38 


38 


38 






33 


39 


39 


39 





34 
37 
38 
89 



13 



If the selected cards are in this case C and 
a, we have for the number 8 + 5 — 1=7, if the 
cards are (7, D and a, we have 5 + 10 — 1 = 14, 
and similarly for other combination of cards. 

Introducing another positive card (F) whose 
value is 40, we shall embrace all numbers up to 
79. In this case, however far we extend our 
numbers, there will be but one negative card (a) 
whose value is —1. 

So far as I am aware, cases II, III and lY, 
which require subtraction as well as addition, 
have never before been noticed. Case I, is on 
many accounts the most interesting, it will em- 
brace more numbers, with fewer cards than in 
either of the other cases. But as a Puzzle to 
those not in the secret of the arrangement of the 
groups of terms, case II is the most remarkable. 
For, if we omit the letters and the brackets, 
which we have employed to assist in their ex- 
planation, and write simply the numbers, wx 
shall have a set of cards, which would afford 
considerable amusement. 

It is obvious that we might employ instead of 
these numbers, individual names of things, as 
the names of distinguished persons, locahties, or 
events, having each individual numbered, so that 
the particular name selected on any card may be 
readil;^ determined by means of its corresponding 
number. 



14 



The following list of the names of 121 Poets 
are thus arranged alphabetically, and each indi- 
vidual is denoted by the appropriate number as 
here given : 

In this case we have five positive cards, denoted 
by the capital letters i5, C, D and E, having 
the corresponding values 1, 3, 9, 27 and 81 ; and 
four negative cards^ denoted by the small letters 
a, &, c and cZ, and having the corresponding nega- 
tive values of —1, —3, —9 and ~2t. J 

These nine cards with the Key Card, are corl 
rectly arranged and given on the following pageJ 
in such a manner as to admit of being cut ouj 
and pasted upon card paper so as to save th J 
labor of copying them with the pen. 1 

If an individual is requested to select such 
cards as contain the name of his iav(>rite Poet, 
and he should return the cards denoted by J, 0, 
and we should at once have by adding the 
values of these cards 1 + 9 + 81 = 91, then re- 
ferring to^our Keij Card, we see that Read cor- 
responds to the number 91. Had he returned 
us the cards A, E and c?, we should have found 
1+81 — 27 = 55 which corresponds to Horace. 

Similarly, the cards D, E, h and c, give 
27 + 81 — 3— 9=96, corresponds to Shakespeare, 
The cards B, E and c, give 3 + 81 — 9=75, cor- 
responding to Milton. 



KEY CARD. 



1. Addison. 

^. Akenside, 

3. Aldrich, 

4. St. Ambrose, 

5. Anecreon, 
Angelo, 

7. Baillie. 

8. Barbauld. 

9. Baxter. 

10. Beattie. 

11. Beaumont, 

12. Blake, 

13. Bowles, 

14. Browning, 

15. Burns, 
!»;. Butler, 

17. Byron, 

18. Callistratus, 

19. Chatterton, 

20. Chaucer, 

21. Coleridge, 
2i. Collins, 
23. Cornwall, 
94. Cowley. 

25. Cowper, 

26. Crabbe, 

27. Croly, 

28. Cunningham, 

29. Daniel, 

30. Davidson, 

31. Dickens, 

32. Doddridge, 
as. Drake, 

34. Dryden, 

35. Eastman, 

36. Elliott, 

37. Emerson, 

38. Ferguson, 
29. Fletcher, 

40. Fortunatus, 

41. Gay, 



42. Oilman. 

43. Glen, 

44. Goethe, 

45. Goldsmith, 

46. Gray, 

47. Heber, 

48. Hemans, 

49. Herbert, 

50. Herrick, 

51. Hogg, 

52. Holmes, 

53. Homer, 

54. Hood, 

55. Horace, 

56. Howitt, 

57. Hugo. 

58. Hunt, 

59. Ingram, 

60. Sam. Johnson, 

61. Ben. Jonson, 

62. Keats, 
6:^. Keble, 

64. Kemble, 

65. Kingsley. 

66. Lamb. 

67. Landor, 

68. Leonidas, 

69. Longfellow, 

70. Lover. 

71. Lowell, 

72. Luther, 

73. Macaulay, 

74. Marvell, 

75. Milton, 

76. Montgomery, 

77. Moore, 

78. Motherwell, 

79. Newton, 

80. Norton, 

81. Ogilvie, 

82. Percival, 



83. Pierpont, 

84. Poe, 

85. Pollok, 

86. Pope, 

87. Prentiss, 

88. Quarles, 

89. Raleigh. 

90. Ramsey, 

91. Read, 

92. Rogers, 

93. Roscoe, 

94. Sappho, 

95. Scott, 

96. Shakespeare, 

97. Shelly, 

98. Shenstoue, 

99. Southey, 

100. Spencer, 

101. Street, 

102. Suckling, 

103. Swift. 

104. Taylor. 

105. Tennyson, 

106. Terry, 

107. Thackeray. 

108. Thomson. 

109. Tuckerman, 

110. Uhland. 

111. Vaughn, 

112. Virgil, 

113. Watta, 

114. Wesley. 

115. White, 

116. Whittier, 

117. AVillis, 

118. Wilson, 

119. Wordsworth, 

120. Young, 

121. Zedlitz. 



16 



(A) 



Addison, 


Glen, 


Pollok, 


St. AmbrosG, 


Grav. 


Quarles, 


Baillie, 


Herbert, 


Read, 


Beattio, 


Holmes, 


Sappho, 


Bowles, 


Horace, 


Shelly, 


Butler, 


Hunt, 


Spencer, 


Chatterton, 


Ben. Jonson, 


Swift, 


Collins, 


Kemble, 


Terry, 


Cowper, 


Landor, 


Tuckerman, 


Cunningham, 


Lover, 


Virgil, 


Dickens, 


Macaula}^, 


White, 


Dry den. 


Montgomery, 


AVilsou, 


Emerson, 


Newton, 


Zedlitz. 


Fortunatus, 


Percival, 





Akensido, 


Goethe, 


Pope, 


Anacreon, 


Heber, 


Raleigh, 


Barbauld, 


Herrrck, 


Rogers, 


Beaumont, 


Homer, 


Scott, 


Browning. 


Howitt, 


Shenstone, 


Byron, 


Ingram, 


Street, 


Chaucer, 


Keats, 


Taylor, 
Thackeray, 


Cornwall, 


Ivingsley, 


Crabbe, 


Leonidas, 


Uhland, 


Daniel, 


Lowell, 


Watts, 


Doddridge, 


Marvell, 


Whittier, 


Eastman, 


Moore, 


Wordsworth. 


Ferguson, 


Norton, 




Gay, 


Pierpont, 





17 



Akenside, 

Aldrich, 

St. Ambrose, 

Beaumont, 

Blake, 

Bowles, 

Chaucer, 

Coleridge, 

Collins, 

Daniel, 

Davidson,, 

Dickens, 

Ferguson, 

Fletcher, 



Anacreon, 

Angelo, 

Baillie, 

Browning, 

Burns, 

Butler, 

Cornwall, 

Cowley, 

Cowpor, 

Doddridge, 

Drake, 

Dryden, 

Oay, 



(B) 

Fortunatus, 

Heber, 

Hemans, 

Herbert, 

Howitt, 

Hugo, 

Hunt, 

Kingsloy, 

Lamb, 

Landor, 

Marvell, 

Milton,; 

Montgomery, 

Pierpont, 



Poe, 

Pollok, 

Rogers, 

Roscoe, 

Sappho, 

Street, 

Suckling, 

Swift, 

Uhland, 

Yaughn, 

Virgil, 

Wordsworth, 

Young, 

Zedlitz. 



(b) 

Oilman, 

Glen, 

Herrick, 

Hogg, 

Holmes, 

Ingram, 

Sara. Johnson, 

Ben. Jonson, 

Leonidas, 

Longfellow, 

Lover, 

Moore, 

Motherwell, 



Newton, 

Pope, 

Prentiss, 

Quarles, 

Scott, 

Shakespeare, 

Shelly, 

Taylor, 

Tennyson, 

Terry, 

Y^atts, 

Wesley, 

White. 



18 



(C) 





TvAvm 1 or»n 
J? t?J ^LiaULij 






T^l Atr*h fir 


Tt a m a ATr 


"Rnillip 


"Pnr f n rt Q f n c! 

X Ul tULlcl Lllr>^ 


Read 


Barbduld, 


Ingram, 


Rogers, 








"Rpof tip 




Sappho, 


Bosiimont 








Keble! 




Bowles, 


Kemble, 


White, 


Doddridge, 


Kingsley, 


Whittier, 


Drake, 


Lamb, 


Willis, 


Dry den, 


Landor, 


Wilson, 
AVords worth 


Eastman, 


Pope, 


Elliott, 


Prentiss, 


Young, 


Emerson, 


Quarles, ' 


Zedlitz. 



(c) 



Browning, 


Goethd, 


Marvell, 


Burns, 


Goldsmith, 


Milton, 


Butler, 


Gray, 


Montgomery, 


Byron, 


Heber, 


Scott, 


Callistratus, 


Hemans, 
Herbert, 


Shakespeare, 


Ohatterton, 


Shelly, 


Chaucer, 


Leonidas, 


Shenstone, 


Coleridge, 


Longfellow, 


Southe}-^, 


Collins, 


Lover, 


Spencer, 


Gay, 


Lowell, 


Street, 


Gilman. 


Luther, 


Suckling, 


Glen, 


Macaulay, 


Swift. 



19 



(D) 

Brownings, Doddridge, Taylor, 

Burns, Drake, Tennyson, 

Butler, Dryden, Terry, 

Byron, Eastman, Thackeray, 

Calistratus, Elliott, Thomson, 

Chatterton. Emerson, Tuckerman, 

Chaucer, Ferguson, Uhland, 

Coleridge, Fletcher, Vaughn, 

Collins, Fortunatus, Virgil, 

Cornwall, Scott, Watts, 

Cowley, Shakespeare, Wesley, 

Cowper, Shelly, White, 

Crabbe, Shenstone, Whittier, 

Croly, Southey, Willis. 

Cunningham, Spencer, AVilson, 

Daniel, Street, Wordsworth, 

Davidson, Suckling, Yoang, 

Dickens, Swift, Zedlitz. 



Gay. 
Oilman, 


Herrick, 


Ingram, 


Hogg, 


Sara. Johnson, 


Glen, 


Holmes, 


Ben. Jonson, 


Goethe, 


Homer, 


Keats, 


Goldsmith, 


Hood, 


Keble, 


Gray, 


Horace, 
Howitt, 


Kemble, 


Heber, 


Kingsley, 


Heman3, 


Hugo, 


Lamb, 


Herbert, 


Hunt, 


Landor, 



20 



Gay, 

Gilman, 

Glen, 

Goethe, 

Goldsmith, 

Gray, 

Heber, 

Hemans, 

Herbert, 

Herrick, 

Hogg, 

Holmes, 

Homer, 

Hood, 

Horace, 

Howitt, 

Hugo, 

Hunt, 

Ingram, 

Sam. Johnson, 

Ben. Jonson, 

Keats, 

Keblo, 

Kemble, 

Kingsley, 

Lamb, 

Landor, 



(E) 

Leonidas, 

Longfellow, 

Lover, 

Lowell, 

Luther, 

Macaulay, 

Marvell, 

Milton, 

Montgomerj^, 

Moore, 

Motherwell, 

Newton, 

Norton, 

Ogilvie, 

Percival, 

Pierpont, 

Poe, 

Pollok, 

Pope, 

Prentiss, 

Quarles, 

Ealeigh, 

Ramsey, 

Read, 

Rogers, 

Roscoe, 

Sappho, 



Scott, 

Shakespeare 

Shellejr, 

Shenstone, 

Southey, 

Spencer, 

Street, 

Suckling, 

Swift, 

Taylor, 

Tennyson, 

Terry, 

Thackeray, 

Thomson, 

Tuckerman, 

Uhland, 

Vaughn, 

Yirgil, 

Watts, 

Weslej^, 

White, 

Whittier, 

Willis, 

Wilson, 

Wordsworth 

Young, 

Zedlitz, 



21 



I will give the following curious mechanical 
method of performing the addition and subtrac- 
tion of the terms of the geometrical progression 
1, 8, 9, 27, 81, without mental effort. 

Prepare 18 square cards of 121 cells each, that 
is of 11 rows of 11 cells in each row, and locate 
the 121 numbers in these cells, in numerical 
order, or in any other order we please, but the 
same order of location must be observed for the 
18 cards. 

Cut out the numbers on one of these squares 
which are given on the card A, and denote the 
square card thus cut or perforated by A A. Also 
make its comphraentary perforated card from one 
of our 18 cards, by cutting out all the numbers 
except those given on A, and call the resulting 
card AAA. Similarly, cut out from another of 
our 18 cards, such numbers as are found on the 
card a, and call the result aa, also form its com- 
plementary card denoted by aaa, by cutting out 
from one of our 18 cards, all the numbers except 
those on the card a. Proceed in the same way 
to form the card BB, and its complementary card 
BBB; also, hh and hbh ; also, CC and COC; 
also, CC and ccc ; also, BI) and BBB ; also, dd 
and ddd] also, ^^and FEE. 

We shall thus obtain 9 new perforated cards 
denoted by AA, aa, BB, bh, CC, cc, DD, dd, EE, 
and their 9 corresponding complementary cards 
AAA.aaa, BBB, Ub,^ CCC, ccc, DDD, ddd, EEE, 

Now if a number is selected w^hich is on the 
cards A^ B, c, and d, and not on any of the other 



22 



cards, we take of the perforated cards, the cards 
AAf BB, cc, dd, and the complementary cards 
aaa, bbb, GGC, BDD, EEE, and placing them 
together in any order, we have a pack of 9 per- 
forated cards, and we shall find one and only one 
perforation extending entirely through the pack, 
and this corresponds with the number sought, 
and by placing our pack upon a square card 
which has none of its numbers cut out, the num- 
ber sought will be revealed through this perfora- 
tion. Jk J 

Since by this arrangement, we never superirflf I 
pose any card on its complementary card, we may 
combine our 18 perforated cards so as to have 
only 9 distinct cards, the upper and lower halves 
of each card being complementary to each other ; 
and adding to these 9 cards, the corresponding 
cards denoted by A, a, B, b, (7, c, B, d and 
we shall have, including the Key Card which j 
contains all the numbers and is not perforated, i| 
10 cards. Each example may be performed by 
placing the 9 cards together upon the Key Card, j 
The only thing to be careful to observe is to turn I 
over, face downwards, such cards as do not con- 
tain the number under consideration. 

Such perforated cards would obviously form | 
considerable amusement when exhibited for the , 
first time. 



(A) 



1 


64 


4 


67 


1 


70 


10 


73 


13 


76 


16 


79 


19 


82 


22 


85 


25 


88 


28 


91 


31 


94 


34 


97 


37 


100 


40 


103 


43 


100 


46 


109 


49 


112 


52 


115 


55 


118 


58 


121 


61 





2 


62 


5 


65 


8 


68 


11 


71 


14 


74 


17 


' 77 


20 


80 


23 


83 


26 


86 


29 


89 


32 


92 


35 


95 


38 


98 


41 


101 


44 


104 


47 


107 


50 


110 


53 


118 


56 


116 


59 


119 



(B) 



9 


65 


•J 

o 


l)D 




O i 


1 i 


>7 1 

/ 4: 


1 z 


75 




i o 




c 

oo 


O 1 
Z 1 


O'i 


zz 




zy 


y z 


oU 


yo 


Q 1 

O 1 


yi 


oc5 


1 A 1 
1 Ul 




1 AO 


40 


103 


47 


110 


48 


111 


49 


112 


56 


119 


57 


120 


58 


121 



(b) 



D 


O 1 





Do 


7 


AO 


1 A 


i u 


J O 


t < 


i 


'70. 


Zo 


7 Q 


Zi 


oo 


ZO 


o / 


OZ 


QQ 

oo 


QQ 
OO 


JO 




96 


/I 1 


07 

y / 


d.9 


1 ni 

L U't 


43 


105 


50 


106 


51 


113 


52 


114 


59 


115 


60 





(C) 



5 


64 


6 


65 




66 


8 


67 


9 


86 


10 


87 


11 


88 


12 


89 


13 


90 


32 


91 


33 


92 


34 


98 


36 


94 


36 


113 


37 


114 


38 


115 


39 


116 


40 


117 


59 


118 


60 


119 


61 


120 


62 


121 


63 





(c) 



14 


68 


15 


69 


16 


70 


17 


71 


18 


72 


19 


78 


20 


74 


21 


76 


22 


76 


41 


95 


42 


96 


43 


97 


44 


98 


45 


99 


46 


100 


47 


101 


48 


102 


49 


103 



(D) 



14 


95 


15 


96 


16 


97 


17 


98 


18 


99 


19 


100 


20 


101 


21 


102 


22 


103 


2B 


104 


24 


105 


25 


106 


26 


107 


27 


108 


28 


109 


29 


110 


30 


111 


31 


112 


32 


113 


33 


114 


34 


115 


35 


116 


36 


117 


37 


118 


38 


119 


39 


120 


40 


121 



41 


54 


42 


55 


43 


56 


44 


57 


45 


58 


46 


59 


47 


60 


48 


61 


49 


62 


50 


63 


51 


64 


52 


65 


53 


66 




67 



31 







(E) 




41 


61 


81 


101 


42 


62 


82 


102 


43 


63 


83 


103 


44 


64 


84 


104 


45 


65 


86 


105 


46 


66 


86 


106 


47 


67 


87 


107 


48 


68 


88 


108 


40 


69 


89 


109 


50 


70 


90 


110 


51 


71 


91 


111 


52 


72 


92 


112 


53 


73 


93 


lis 


54 


74 


94 


114 


55 


75 


95 


115 


56 


76 


96 


116 


'57 


77 


97 


117 


58 


78 


98 


118 


59 


78 


99 


119 


.60 


80 


100 


120 
121 



EXPLANATION. 

The five cards denoted 
by the capital letters A, 
B, C, D and E all end 
with the number 121, 
and the value of each 
is positive and requires 
to be added. These val- 
ues are as follows : 

A=l; B=3; C=r9; 
D=27; E=:81. 

The four cards de- 
noted by the small let- 
ters a, 5, c and d are 
negative^ and their val- 
ues are to be subtracted. 
These values are as fol- 
lows : 

a- -1; b= -3; 
0= -9; d- -27. 

EXAMPLES. 

A, B, C give 
1-1-3 + 9 = 13. 

A, E, b give 

1 + 81-3 = 79. 

B, D, a, c give 

8 + 27-1-9 — 20. 

E, a, b, c, d give 
8i_l_3^9-^i7=:41 



^1 

I 



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